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# Fundamentals of Physics Chapter 10 Solutions: Rotation

Halliday Resnick and Walker Fundamentals of Physics Volume 1 Solutions for Chapter 10 ‘Rotation’ discusses all the exercises of the chapter thoroughly that will help you in CBSE and competitive exams. The chapter of Resnick Halliday Solutions describes the principles of rotation and its formulas or theorems. In this chapter, you will also study some of the major concepts of rotational variable like angular position, angular displacements, angular velocity and speed, angular acceleration, kinetic equations, rotational kinetic and rotational inertia, the parallel axis theorem, torque, Newton’s second law in angular form, and work and rotational kinetic energy.

All these concepts discussed in Resnick Halliday & Walker Fundamentals of Physics Extended Volume 1 Rotation are crucial to study for exams. The questions given in this chapter are based on the latest CBSE Physics topics and JEE Physics concepts. There are a total 9 modules that comprises overall 108 questions. These questions help you to practice the entire concepts that are discussed in the chapter.

Instasolv provides you with the online solutions for all problems given in the Resnick Halliday and Walker Fundamentals of Physics Volume 1 Rotation for CBSE Class 11. The solutions are effective and our experts make sure that they are easy to understand as well. The chapter should be understood thoroughly and holds major importance in case you are planning for competitive level exams like IIT JEE or NEET. Instasolv solutions will help you save a lot of time while studying.

## Important Topics for Resnick Halliday and Walker Fundamentals of Physics Volume 1 Solutions Chapter 10: Rotation

Rotational Variables

• Angular position

To discuss the rotation of a body that is rigid and has a fixed axis, we generally assume that the axis line is fixed in the body perpendicular to that axis and is rotating with the body. To measure the angular position Θ of this line relative to a fixed direction. It is measured as

Θ= s/r

In this s stands for the arc length of a circular path with radius r.

• Angular displacement

A body rotating about the rotation axis by changing its angular position from Θ1 to Θ2 undergoes angular displacement.

ΔΘ = Θ1 + Θ2

• Angular Velocity

When a body rotates through an angular displacement in an interval, then it is angular displacement velocity. It is given by:

ωavg = ΔΘ/Δt

• Angular acceleration

When the angular velocity changes from ω1 to ω2 in a time interval, the average angular acceleration of a body is given by:

aavg =    ω2 – ω1 / t2 t1 =  Δω/ Δt

Linear and Angular Variables

A point is a rotating body that is also rigid, at a perpendicular distance from the rotation axis moves in a circle having the radius r. In case the body rotates through an angle Θ, the point moves along an arc with length s given by:

s = Θr

The linear velocity when Θ is in radians and ω is the angular speed with radius r is given by:

v= ωr

Rotational Kinetic Energy Kinetic energy of a body that is rigid and rotating about a fixed axis is given as:

K = ½ Iω2

Where I is Rotational Inertia.

The Parallel Axis Theorem

In this theorem, the rotational inertia of a body about any axis is related to the same body about the parallel axis through the center of mass.

I = Icom  + Mh2

Torque

The turning or twisting action on a body about a rotation axis due to a force is referred to as torque. The SI unit of torque is the newton-meter (N.m).

Newton’s Second Law in Angular Form

The rotational analogue of newton’s second law is given by:

### τnet = Iα

Here,τ is the net torque acting on a rigid body, I is the rotational inertia and α is the angular acceleration.

### Exercise Discussion of Resnick Halliday & Walker Fundamentals of Physics Volume 1 Solutions Chapter 10: Rotation

Module 1: Rotational variables

This module comprises over 8 questions related to rotational revolutions. This includes questions like finding how many rotations a ball makes on its way to home plate or defining angular speed. You will also find questions on calculating the angular velocity.

Module 2: Rotation with Constant Angular Acceleration

In this module there are a total of 9 questions which covers the entire topic of angular acceleration. The questions include calculating the constant angular acceleration of a flywheel, time required to complete the given revolutions, the angular acceleration in revolutions per minute squared and so on.

Module 3: Relating the linear and Angular Variables

There are net 13 questions in this module. By solving these questions, you will be able to find the average angular speed of the tower’s top about its base, linear speed of the point on the rim of the flywheel and the least coefficient of static friction to avoid slippage.

Module 4: Kinetic Energy of Rotation

There are just 2 questions in this module in which you will have to answer what is the magnitude of a rod’s angular acceleration and its kinetic energy. In question 2, you have to calculate the rotational inertia of the wheel that has the given kinetic energy.

Module 5:  Calculating the Rotational Inertia

In this module there are 9 questions in all and these questions are based on calculating the rotational kinetic energy and the rotational inertia.

Module 6: Torque

There are a total of 4 questions in this module based on the entire concept of torque. You will be answering questions like what is the net torque about the pivot, what is the magnitude of the gravitational torque calculated about the pivot, etc.

Module 7: Newton’s Second law of Rotation

This module comprises overall 9 questions related to the magnitude of average angular acceleration, average external torque, and the rotational inertia of the plate about the axle.

Module 8: Work and Rotational Kinetic Energy

The module has an overall 10 questions. These questions are based on the topics of conservation principles, rotating speed and rotating torque, power etc.